Theorem eqeq1i

Description: Inference from equality to equivalence of equalities. (Contributed by NM, 15-Jul-1993)

	Ref	Expression
Hypothesis	eqeq1i.1	|- A = B
Assertion	eqeq1i	|- ( A = C <-> B = C )

Proof

Step	Hyp	Ref	Expression
1		eqeq1i.1	|- A = B
2		eqeq1	|- ( A = B -> ( A = C <-> B = C ) )
3	1 2	ax-mp	|- ( A = C <-> B = C )